# In trapezoid ABCD BC and AD base, AD = 10cm, BC = 5cm, AC = 9cm, BD = 12cm. Find the area of the trapezoid.

The triangles BOC and AOD are similar in two angles, since the angle BOC = AOD as vertical angles, the angle BOC = BDA as criss-crossing angles. The coefficient of similarity of triangles is: K = BC / AD = 5/10 = 1/2.

Then OB / OD = 1/2.

2 * BО = DO. DO + BO = 12 cm.

2 * BО + BО = 12 cm.

BO = 4 cm, BO = 8 cm.

Similarly, ОC = 3 cm, ОА = 6 cm.

In the triangle BOC, the Pythagorean theorem holds, BC ^ 2 = OB ^ 2 + OC ^ 2.

25 = 16 + 9.

Then the triangles BOC and AOD are rectangular.

Let’s draw the KН height through the point of intersection of the diagonals.

Then KO = ОВ * ОC / ВC = 4 * 3/5 = 12/5 = 2.4 cm.

HO = OA * OD / AD = 6 * 8/10 = 4.8 cm.

Then KН = KO + KН = 2.4 + 4.8 = 7.2 cm.

Determine the area of ​​the trapezoid.

Savsd = (BC + AD) * KН / 2 = (5 + 10) * 7.2 / = 54 cm2.

Answer: The area of ​​the trapezoid is 54 cm2. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.